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Check the connections at the relay. Very common issue
That's because the fault is probably the inline fuse holder in the 10-ga orange wire where it connects to the firewall junction block. The high blower fuse is notorious for overheating due to degraded electrical connections, which melts the fuse holder, which degrades electrical connections of the fuse even further until, eventually, no connection remains. Temporarily use a 10- or 12-ga jumper wire to bypass the fuse holder and restore power directly to the relay, then try the high blower using the dash fan switch to see what happens. If high blower function is restored, replace the inline fuse holder and fuse using a 20-amp ATO/ATC style that has a dust cover. Post the results and we will continue from there, if necessary.
Does the wiring need to be 10 gauge or can I use 12 gauge which I have?